TY  - JOUR
A1  - Hack, Thomas-Paul
A1  - Hanisch, Florian
A1  - Schenkel, Alexander
T1  - Supergeometry in Locally Covariant Quantum Field Theory
JF  - Communications in mathematical physics
N2  - In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor U : SLoc -> S*Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct superquantum field theories in terms of enriched functors eU : eSLoc -> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1 vertical bar 1-dimensions and the free Wess-Zumino model in 3 vertical bar 2-dimensions.
Y1  - 2016
U6  - https://doi.org/10.1007/s00220-015-2516-4
SN  - 0010-3616
SN  - 1432-0916
VL  - 342
SP  - 615
EP  - 673
PB  - Springer
CY  - New York
ER  -